Direct versus indirect many-body methods for calculating vertical electron affinities: applications to F−, OH− , NH2−, CN−, Cl−, SH− and PH2−

Electron propagator theory (EPT) is applied to calculating vertical ionization energies of the anions F⁻, Cl⁻, OH⁻,SH⁻, NH₂⁻, PH₂⁻ and CN⁻. Third-order and outer valence approximation (OVA) quasiparticle calculations are compared with ΔMBPT(4) (MBPT, many-body perturbation theory) results using the same basis sets. Agreement with experiment is satisfactory for EPT calculations except for F⁻ and OH⁻, while the ΔMBPT treatments fail for CN⁻. EPT(OVA) estimates are reliable when the discrepancy between second- and third-order results is small. Computational aspects are discussed, showing relative merits of direct and indirect methods for evaluating electron binding energies.     

On the adequacy of the molecular-orbital picture for describing ionization processes

General arguments concerning the adequacy of the molecular-orbital (MO ) ionization picture are given. Whereas the MO ionization picture is found to be valid for both outer valence and core electrons, it may completely break down in the inner valence region. The general considerations are supported by many-body calculations on methane, acetylene, hydrogen cyanide, and dinitrogen tetroxide. It is demonstrated that the breakdown of the MO ionization picture is a common phenomenon.     

An ab initio CI study of the ground and excited states of p-quinodimethane

Configuration interaction (CI) studies of the ground, electronically excited singlet and triplet states and of the ionized states (cations) are reported for p- quinodimethane (p-xylylene). The calculated ionization potentials are compared with the experimental photoelectron spectrum for the low-energy ionization region. The two high-energy low-intensity flanks of the second and third band observed in the photoelectron spectrum are assigned to be due to the two non-Koopmans' cation states, ascribing to shake-up ionizations.The calculated singlet-singlet and singlet-triplet excitation energies are compared with previous semiempirical MO results and experimental data.     

Correlation energies in open shell systems. Comparison of CEPA,PNO-CI and perturbation treatments based on the restricted Roothaan-Hartree-Fock formalism

A set of simple molecules in closed and open-shell ground states is treated by the three techniques mentioned in the title, using the same geometries and basis sets (DZ + P). It is found that for nearly all molecules treated in this study (exceptions are H₂ and CH₃) consistently about 98% of the CEPA valence shell correlation energy is obtained by third-order many-body Ray-leigh-Schrödinger perturbation theory (MB-RSPT). The CEPA and MB-RSPT results for reaction energies and barrier heights for some simple reactions differ by 0 to 30 kJ/mol, the CEPA results being in most cases closer to experiment than MB-RSPT, while CI results are much less reliable as long as CI is limited to singly and doubly substituted configurations only.     

Static dipole polarizabilities of open-shell negative ions

Summary Dipole polarizability estimates at have been calculated for the 2p and 3p open-shell negative ions in their ground and valence excited states. To complete the sequence such estimates for F^– and Cl^– in their ground¹ S state have also been made. Single configuration based linear response theory has been adopted presently with a view to study the effect of RPA-type correlations on the polarizabilities of such systems. For the 3p open-shell systems the innermost 1s core has been kept frozen. Most of the results are reported for the first time. Agreement with existing data, wherever available, is reasonable. The convergence of the polarizability estimates towards basis sets has been studied.     

Shake-up peak positions and intensities by many-body theory methods

The valence shell X-ray photoelectron spectrum of N₂ is calculated using the equations-of-motion—Green's function method. The inclusion of shake-up basis operator configurations in the primary operator space along with the simple ionization operator configurations allows for the calculation of shake-up peak positions on an equal footing with the simple ionization energies. The important shake-up basis operator configurations are identified using configuration selection techniques similar to those which have been successfully employed in large scale configuration interaction problems, thus minimizing the size of the matrices to be diagonalized. The relative peak intensities are calculated within the plane wave approximation. The intensity equations are analyzed indicating that the relative peak intensities are more sensitive to ground state correlation effects than the peak positions. Modifications of the theory to improve the calculations of shake-up energies are discussed.     

Comparison of MBPT and coupled-cluster methods with full CI. Importance of triplet excitation and infinite summations

Results from full fourth-order perturbation theory [SDTQ MBPT(4)], and the coupled-cluster single- and double-excitation model (CCSD). are compared with recent full CI results for BH, HF, NH₃, and H₂O. For H₂O, studies include large symmetric displacements of the OH bonds, which offer a severe test for any single-reference MBPT/CC method. In every case. CCSD plus fourth-order triple-excitation terms provide agreement with the full CI to < 2 kcal/mole. SDTQ MBPT(4) has an error 10 kcal/mole for displaced H₂O.     

A note on the convergence of multiconfigurational many-body perturbation theory

The convergence of multiconfigurational many-body perturbation theory (MC MBPT ) is discussed in connection with the intruder state. Its convergence properties are first examined with a fictitious three-level system employing a Hermitian version of MC MBPT , which permits a general model space. It is then applied to the H₂—H₂ and N₂ systems. The results suggest that a more extensive model space is likely to embrace new intruder states and the space extension be executed with due caution.     

Information theoretic indices for characterization of chemical structures. By Danail Bonchev Wiley,New York, 1983

Wilson, Jankowski, and Paldus have recently applied nondegenerate many-body perturbation theory (MBPT ) to simple models, in which the degree of quasidegeneracy could be varied continuously, and concluded that the nondegenerate theory was applicable even near degeneracy. The error in their results changes, however, considerably with geometry, leading to an incorrect potential surface. An extension of their calculations shows convergence even at exact degeneracy (square planar H₄). It is shown here that the apparently good convergence is due to the suppression of the large (infinite at exact degeneracy) component of the perturbation energy in low order by the way the Hamiltonian is partitioned. This component will, however, resurface at higher orders, leading to slow convergence or even divergence. The low-order sum of the perturbation series is not very meaningful, depends strongly on details of the zero-order Hamiltonian, and yields, in general, incorrect potential surfaces. Multireference MBPT eliminates these problems.     

Near-degeneracy effects and efficiency of MBPT calculations of molecular properties. Polarizability curve of H2

The polarizability curve of H₂ is calculated by using the finite-field perturbation method. All self-consistency effects are accounted for at the HF level and many-body perturbation theory (MBPT) is used to evaluate the correlation contributions. Using a single HF determinant as a reference in MBPT calculations makes the near-degeneracy effects of essential importance on increasing the interatomic distance. Nevertheless, applying the MBPT scheme with appropriate fourth-order terms gives nearly exact values of both components of the polarizability tensor for interatomic distances up to ≈3.6 au.     

A unitary group formulation of many-body theory: Diagram systematics and use of the spin shifts

This paper shows that the spin-shift formalism developed in B. T. Pickup and A. Mukhopadhyay [Int. J. Quantum Chem. 26 , 101 (1984)] supports a one-component diagrammatics which has a systematics akin to that in the spin-orbital many-body theory. The diagrams are neither Goldstone nor Yutsis type, and characterize the chain U(2R) ? U(R)?SU(2) on which the spin-shift formalism is based. Accordingly, while the lines in such diagrams are labeled by the orbital indices, the diagram structure adequately reflects the irreducible representation of the group U(R). In this sense the paper presents a unitary group approach to the natural generalization of the usual many-body theory for the spin-adapted cases. A set of very simple rules is derived; their similarity with the corresponding rules in the ordinary many-body theory and practical utility are discussed in connection with (a) matrix elements over many-electron spin states and (b) closed- and open-shell many-body perturbation theory. A possibility of integral-driven many-body perturbation theory for open-shells is indicated. Connections of this formalism with others are also discussed.     

SAC-CI general-R study of the ionization spectrum of HCl

The valence ionization spectrum of HCl is studied by symmetry-adapted-cluster configuration-interaction general-R and SD-R methods. The general-R method describes well the peak positions and intensities of seven satellite lines observed below the double ionization threshold. The twinning shake-up states due to the (4σ)⁻¹ state and the Rydberg states of HCl⁺ are correctly reproduced. Received: 26 June 1998 / Accepted: 9 September 1998 / Published online: 8 February 1999     

Dyson orbitals for ionization from the ground and electronically excited states within equation-of-motion coupled-cluster formalism: theory, implementation, and examples

Implementation of Dyson orbitals for coupled-cluster and equation-of-motion coupled-cluster wave functions with single and double substitutions is described and demonstrated by examples. Both ionizations from the ground and electronically excited states are considered. Dyson orbitals are necessary for calculating electronic factors of angular distributions of photoelectrons, Compton profiles, electron momentum spectra, etc, and can be interpreted as states of the leaving electron. Formally, Dyson orbitals represent the overlap between an initial N-electron wave function and the N-1 electron wave function of the corresponding ionized system. For the ground state ionization, Dyson orbitals are often similar to the corresponding Hartree-Fock molecular orbitals (MOs); however, for ionization from electronically excited states Dyson orbitals include contributions from several MOs and their shapes are more complex. The theory is applied to calculating the Dyson orbitals for ionization of formaldehyde from the ground and electronically excited states. Partial-wave analysis is employed to compute the probabilities to find the ejected electron in different angular momentum states using the freestanding and Coulomb wave representations of the ionized electron. Rydberg states are shown to yield higher angular momentum electrons, as compared to valence states of the same symmetry. Likewise, faster photoelectrons are most likely to have higher angular momentum.     

Ground states of molecules. 56. MNDO calculations for molecules containing sulfur

MNDO has been extended to sulfur, but without inclusion of 3d AO s. Calculations are reported for heats of formation, geometries, dipole moments, and ionization energies of a variety of sulfur-containing molecules. The average discrepancy between calculated and observed heats of formation is larger than for compounds of other elements, a difference probably due, at least partly, to the lower accuracy of the thermochemical data for sulfur compounds. The calculated dipole moments agree well with experiment as do the calculated ionization energies, except for those corresponding to ionization from sulfur “lone-pair” orbitals which are too high by ca. 1 eV, probably as a result of the neglect in NDDO of interactions between inner and valence shell orbitals. As in the case of other third-period elements, the calculated heats of formation of compounds of sulfur in its higher valence states (S^IV, S^VI) were too positive by large amounts, due presumably to the neglect of 3d AO s.     

Temperature effects in x-ray photoelectron spectra of paramagnetic cupric and iron complexes with anomalous magnetic properties

The temperature dependence of the XPS spectra of paramagnetic cupric and iron complexes with anomalous magnetic properties is studied. It was found that the XPS spectra of polynuclear complexes with antiferromagnetic interaction, such as cupric acetate, do not change with temperature, although their magnetic moments diminish essentially. The Fe 2p spectra of mononuclear iron (III) complexes with the spin multiplicity transitions S = $\text{1}\text{2}$ ? S = $\text{5}\text{2}$ exhibit temperature-dependent reversible alterations of shake-up satellite intensity which correlate with the spin state of the paramagnetic Fe(III) ion. The results obtained prove the mechanism of appearance of intensive shake-up satellites in XPS spectra of paramagnetic 3d element complexes, which relates shake-up excitations with the interaction of the photoelectron with unpaired valence 3d electrons during photoionization.     

Open-Shell coupled-cluster method: Variational and nonvariational calculation of ionization potentials

A hermitian, variational open-shell coupled-cluster method is described and applied to the calculation of H₂O and N₂ ionization potentials in the _T ≈ T₂ approximation. A nonvariational calculation is also carried out, with the inclusion of T₁ and T₃ in addition to T₂. Both methods give fair agreement with experiment when only T₂ is taken into account. T₃, which is included at present in the nonvariational scheme only, has a considerable effect on the results and gives good agreement with experiment.     

Core polarization and relativistic effects competition in the first ionization potentials for some systems in the Cu,Ag, and Au isoelectronic sequences

Single-configuration relativistic Hartree–Fock values of the first ionization potentials for Cu through Kr⁷⁺, Ag through I⁶⁺, and Au through Pb³⁺ are computed in “frozen” and “relaxed core” approximations with and without allowance for core polarization. Effects of polarization of the atomic core by the valence electron are included by introducing a polarization potential in the one-electron Hamiltonian of the valence electron. The core polarization potential depends on two parameters, the static dipole polarizability of the core α and the cut-off radius r₀, which are chosen independently of the ionization potential data. It is demonstrated that by including the core polarization potential with α and r₀ parameters, which are simply chosen instead of being empirically fitted, it is still possible to account, on the average, for at least 70% of the discrepancy between the single-configuration relativistic Hartree–Fock ionization potentials and the experiment, a discrepancy usually ascribed to the contribution of valence-core electron correlations, and to bring the theoretical ionization potentials to an average agreement with experiment of around 1%. It can be concluded from this study that for low and medium Z elements the core polarization dominates for neutral systems or systems in low ionization stages, whereas for highly ionized systems the relativistic effects prevail. For heavy elements, however, the core polarization influence is comparable to the relativistic one only for neutral systems, whereas for ions the relativistic effects are overwhelmingly predominant.     

High-order electron-correlation methods with scalar relativistic and spin-orbit corrections

An assortment of computer-generated, parallel-executable programs of ab initio electron-correlation methods has been fitted with the ability to use relativistic reference wave functions. This has been done on the basis of scalar relativistic and spin-orbit effective potentials and by allowing the computer-generated programs to handle complex-valued, spinless orbitals determined by these potentials. The electron-correlation methods that benefit from this extension are high-order coupled-cluster methods (up to quadruple excitation operators) for closed- and open-shell species, coupled-cluster methods for excited and ionized states (up to quadruples), second-order perturbation corrections to coupled-cluster methods (up to triples), high-order perturbation corrections to configuration-interaction singles, and active-space (multireference) coupled-cluster methods for the ground, excited, and ionized states (up to active-space quadruples). A subset of these methods is used jointly such that the dynamical correlation energies and scalar relativistic effects are computed by a lower-order electron-correlation method with more extensive basis sets and all-electron relativistic treatment, whereas the nondynamical correlation energies and spin-orbit effects are treated by a higher-order electron-correlation method with smaller basis sets and relativistic effective potentials. The authors demonstrate the utility and efficiency of this composite scheme in chemical simulation wherein the consideration of spin-orbit effects is essential: ionization energies of rare gases, spectroscopic constants of protonated rare gases, and photoelectron spectra of hydrogen halides.     

Ab initio density functional theory applied to quasidegenerate problems

Ab initio density functional theory (DFT), previously applied primarily at the second-order many-body perturbation theory (MBPT) level, is generalized to selected infinite-order effects by using a new coupled-cluster perturbation theory (CCPT). This is accomplished by redefining the unperturbed Hamiltonian in ab initio DFT to correspond to the CCPT2 orbital dependent functional. These methods are applied to the Be-isoelectronic systems as an example of a quasidegenerate system. The CCPT2 variant shows better convergence to the exact quantum Monte Carlo correlation potential for Be than any prior attempt. When using MBPT2, the semicanonical choice of unperturbed Hamiltonian, plays a critical role in determining the quality of the obtained correlation potentials and obtaining convergence, while the usual Kohn-Sham choice invariably diverges. However, without the additional infinite-order effects, introduced by CCPT2, the final potentials and energies are not sufficiently accurate. The issue of the effects of the single excitations on the divergence in ordinary OEP2 is addressed, and it is shown that, whereas their individual values are small, their infinite-order summation is essential to the good convergence of ab initio DFT.     

A spin-adapted coupled-cluster based linear response theory for double ionization potentials

We developed in this article a spin-adapted formulation of the coupled-cluster based linear response theory (CC-LRT) for computing double-ionization potentials (DIPs), which may be experimentally observed by Auger spectroscopy. CC-LRT is a multireference generalization of the CC theory where the energy differences have no disconnected vacuum (core) diagrams, signifying core-extensivity. For the spin-adaptation of the CC-LRT equations for the singlet and triplet manifolds, we used the Young-Yamanouchi orthogonal spin-eigenfunctions. The orbital version of the CC-LRT equations are then automatically generated by the conjugate projection operators of Young-Yamanouchi spin functions. We illustrated the working of our spin-adaptation procedure by confining our CC-LRT equations to the space of 2h and 1p–3h ionized determinants. As numerical application of our formalism, we computed the Auger kinetic energies of HF and H₂O. We also analyzed the nature of size-extensivity of the DIPs generated by CC-LRT and showed explicitly that when the molecule is composed of two noninteracting fragments the computed DIPs are either DIPs of fragment A or B or a composite DIP depending on both A and B, which are just not sum of ionization potentials (IPs) of A and B. This analysis is done to underscore the fact that DIPs from CC-LRT is only core-extensive and not fully extensive. © 1996 John Wiley & Sons, Inc.